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State-Space Control Design

LQG/LQR and pole-placement algorithms

State-space control design methods, such as LQG/LQR and pole-placement algorithms, are useful for MIMO design.

Functions

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lqrLinear-Quadratic Regulator (LQR) design
lqryForm linear-quadratic (LQ) state-feedback regulator with output weighting
lqiLinear-Quadratic-Integral control
dlqrLinear-quadratic (LQ) state-feedback regulator for discrete-time state-space system
lqrdDesign discrete linear-quadratic (LQ) regulator for continuous plant
lqgLinear-Quadratic-Gaussian (LQG) design
lqgregForm linear-quadratic-Gaussian (LQG) regulator
lqgtrackForm Linear-Quadratic-Gaussian (LQG) servo controller
augstateAppend state vector to output vector
normNorm of linear model
estimForm state estimator given estimator gain
placePole placement design
regForm regulator given state-feedback and estimator gains

Topics

Linear-Quadratic-Gaussian (LQG) Design

Linear-quadratic-Gaussian (LQG) control is a state-space technique that allows you to trade off regulation/tracker performance and control effort, and to take into account process disturbances and measurement noise.

LQG Regulation: Rolling Mill Case Study

Use linear-quadratic-Gaussian techniques to regulate the beam thickness in a steel rolling mill.

Design LQG Tracker Using Control System Designer

Design a feedback controller for a disk drive read/write head using LQG synthesis.

Design Yaw Damper for Jet Transport

This case study illustrates the classical design process.

Design an LQG Regulator

Design an LQG regulator for a plant output in a system with noise.

Design an LQG Servo Controller

Design an LQG servo controller using a Kalman state estimator.

Design an LQR Servo Controller in Simulink

Design an LQR controller for a system modeled in Simulink®.

Pole Placement

Closed-loop pole locations have a direct impact on time response characteristics such as rise time, settling time, and transient oscillations. Pole placement uses state-space techniques to assign closed-loop poles.

Featured Examples

DC Motor Control

DC Motor Control

The comparison of three DC motor control techniques for tracking setpoint commands and reducing sensitivity to load disturbances: feedforward command

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Thickness Control for a Steel Beam

Thickness Control for a Steel Beam

Design a MIMO LQG regulator to control the horizontal and vertical thickness of a steel beam in a hot steel rolling mill.

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Regulate Pressure in Drum Boiler

Regulate Pressure in Drum Boiler

Use Simulink® Control Design™ software, using a drum boiler as an example application. Using the operating point search function, the example illustrates model linearization as well as subsequent state observer and LQR design. In this drum-boiler model, the control problem is to regulate boiler pressure in the face of random heat fluctuations from the furnace by adjusting the feed water flow rate and the nominal heat applied. For this example, 95% of the random heat fluctuations are less than 50% of the nominal heating value, which is not unusual for a furnace-fired boiler.

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Control System Toolbox Documentation

Support

Learn how to automatically tune PID controller gains

Learn how to automatically tune PID controller gains

Download code examples